Men in Black was a movie based on a "real" paranormal phenomenon. In 1976, Dr. Herbert Hopkins claimed that a man fitting the classic description of the Men in Black visited him. This is the description from UFO Folklore Center

The man was dressed in a black suit, with black hat, tie and shoes, and a white shirt, "I thought, he looks like an undertaker," Hopkins later said. His clothes were immaculate - suit unwrinkled, trousers sharply creased. When he took off his hat, he revealed himself as completely hairless, not only bald but without eyebrows or eyelashes. His skin was dead white, his lips bright red.

Through the years, many such sightings have taken place (this source claims hundreds) with descriptions of the visitors varying slightly, if at all. Their alleged behavior is very strange, with some carrying seemingly very high-tech equipment, or being astounded at something as mundane as a ball-point pen. They usually arrive shortly after a UFO sighting, presumably to warn the person not to report the sighting (with a good old-fashioned threat to punctuate). 

One of the most famous MiB sightings actually occurred in West Virginia, my home state.

The sightings occurred after a glut of "Mothman" sightings. Here is a description of the Mothman, which was sighted in a few southern West Virginia towns: (excerpted from The Paranormal Project: Mothman) 

...shaped like a man, but bigger." It also boasted bat-like wings which it folded against its back and, notably, two huge red eyes "two inches wide and six inches apart." The thing appeared to have no head, its eyes situated in its "shoulders."...

and this: 

...[the] creature...proceeded to take to the air and keep pace with [the witnesses'] car. ( And this without even flapping its wings!) As it flew overhead the witnesses heard a sound "like a record played at high speed, or the squeak of a mouse." The thing followed them right up to the city limits...

The paranormal explanation for this is that it is either some kind of strange, unidentified animal, or some kind of creature from another dimension. 

The rational explanation is that it is a sandhill crane, which would be consistent with the sightings of the Mothman. 

There is still no rational explanation for Mothman, at least no concrete evidence for its existence. However unlikely, it is much more possible that Point Pleasant was visited upon by a crane than a supernatural visitor. 

Men In Black also lack an explanation. They may be creatures from another dimension as well (which is a very convenient way of "explaining" a paranormal creature without explaining it at all), or they may also be government agents. What they truly are is beyond the scope of the Skeptic, and is yet another mystery that will never be solved to any acceptable degree.

• Agents of the Dark is actually a somewhat reasonable take on the MiB phenomenon, though it is still heavy on the conspiracy paranoia
• Mothman is an excellent treatise on the Mothman phenomenon with both skeptical theories and the (far less believable) paranormal theories...includes the most reputable witness reports.
• Sandhill Crane is a short description of the elusive bird.